Recently I went on a trek to a placed named "Har ki Doon". The trek took us around an altitude of 3500 meters(15000 ft). When we were there, our guide advised us not to cover up our ears. According to him, covering up the ears would increase the time required to acclimatize. At the same time, covering up one's ears keeps the body warm. So is there any validity in not covering up the ears at higher altitudes?
Also, by not covering up the ears, is there a risk of exposing oneself to harmful cold weather?

That's half the fun of hiring a local guide - learning the local way of doing things. Of course, to a certain extent you have to use your own judgement. They undoubtedly know a hell of a lot about their region, terrain, and route, but often aren't as up on their principles of science.

So, in short: No. Covering your ears will not in any way expedite or retard your acclimatization. The forces of atmospheric pressure won't be affected in the least by your head gear -- unless you are wearing a pressure-sealed space-helmet.

At the same time, not covering up can result in frost nip, or frost bite. Your ear lobes have a high surface area making them lose heat rapidly and thus more susceptible to cold injuries. Cover up, buttercup.

Sounds like a myth to me. The only thing that could possibly come into play is the pressure inside your head. But in order to hold the pressure inside your head constant, you would have to plug your ears with something air-tight, not open your mouth, et cetera. I can’t see how a beanie hat or something like that could prevent the outside and inside pressures from equalizing.